No, alternative transport was provided. It’s not a case of having to be the sort of alternative that you happen to want.
That's not exactly the case.
TfL Bus is not under the railway nor paid by the railway, nor national rail tickets are accepted. It can hardly say that the London Night bus is offered by the railway system.
If the railway needs to provide something, they need to arrange the transport or provide the ticket on that kind of transport. It doesn't matter what it is, like bus, coach, taxi, horse-drawn carriage, helicopter, back of a bike, whatever.
Needless to mention, the night bus is not timed to meet the railway, which up to 30 minutes wait to be possible, and need to be waiting in a non-railway public area.
Isn't the issue that the train was provided by South Eastern and not TfL. If it was an Overground service which was cancelled, a TfL bus could be seen as an alternative; surely it would only work in this case if South Eastern had arranged ticket acceptance.
If it is in the system, then surely existing alternative transport is offered by the party.
But, as mentioned, as Southeastern is in wrong this time, and no coordination was made with TfL to arrange ticket acceptance and coordinated bus departure time at New Cross Gate to minimise wait at New Cross Gate Station.